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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.distribution;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.NumberIsTooLargeException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.OutOfRangeException;<a name="line.20"></a>
<FONT color="green">021</FONT>    <a name="line.21"></a>
<FONT color="green">022</FONT>    /**<a name="line.22"></a>
<FONT color="green">023</FONT>     * Base interface for distributions on the reals.<a name="line.23"></a>
<FONT color="green">024</FONT>     *<a name="line.24"></a>
<FONT color="green">025</FONT>     * @version $Id: RealDistribution.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.25"></a>
<FONT color="green">026</FONT>     * @since 3.0<a name="line.26"></a>
<FONT color="green">027</FONT>     */<a name="line.27"></a>
<FONT color="green">028</FONT>    public interface RealDistribution {<a name="line.28"></a>
<FONT color="green">029</FONT>        /**<a name="line.29"></a>
<FONT color="green">030</FONT>         * For a random variable {@code X} whose values are distributed according<a name="line.30"></a>
<FONT color="green">031</FONT>         * to this distribution, this method returns {@code P(X = x)}. In other<a name="line.31"></a>
<FONT color="green">032</FONT>         * words, this method represents the probability mass function (PMF)<a name="line.32"></a>
<FONT color="green">033</FONT>         * for the distribution.<a name="line.33"></a>
<FONT color="green">034</FONT>         *<a name="line.34"></a>
<FONT color="green">035</FONT>         * @param x the point at which the PMF is evaluated<a name="line.35"></a>
<FONT color="green">036</FONT>         * @return the value of the probability mass function at point {@code x}<a name="line.36"></a>
<FONT color="green">037</FONT>         */<a name="line.37"></a>
<FONT color="green">038</FONT>        double probability(double x);<a name="line.38"></a>
<FONT color="green">039</FONT>    <a name="line.39"></a>
<FONT color="green">040</FONT>        /**<a name="line.40"></a>
<FONT color="green">041</FONT>         * Returns the probability density function (PDF) of this distribution<a name="line.41"></a>
<FONT color="green">042</FONT>         * evaluated at the specified point {@code x}. In general, the PDF is<a name="line.42"></a>
<FONT color="green">043</FONT>         * the derivative of the {@link #cumulativeProbability(double) CDF}.<a name="line.43"></a>
<FONT color="green">044</FONT>         * If the derivative does not exist at {@code x}, then an appropriate<a name="line.44"></a>
<FONT color="green">045</FONT>         * replacement should be returned, e.g. {@code Double.POSITIVE_INFINITY},<a name="line.45"></a>
<FONT color="green">046</FONT>         * {@code Double.NaN}, or  the limit inferior or limit superior of the<a name="line.46"></a>
<FONT color="green">047</FONT>         * difference quotient.<a name="line.47"></a>
<FONT color="green">048</FONT>         *<a name="line.48"></a>
<FONT color="green">049</FONT>         * @param x the point at which the PDF is evaluated<a name="line.49"></a>
<FONT color="green">050</FONT>         * @return the value of the probability density function at point {@code x}<a name="line.50"></a>
<FONT color="green">051</FONT>         */<a name="line.51"></a>
<FONT color="green">052</FONT>        double density(double x);<a name="line.52"></a>
<FONT color="green">053</FONT>    <a name="line.53"></a>
<FONT color="green">054</FONT>        /**<a name="line.54"></a>
<FONT color="green">055</FONT>         * For a random variable {@code X} whose values are distributed according<a name="line.55"></a>
<FONT color="green">056</FONT>         * to this distribution, this method returns {@code P(X &lt;= x)}. In other<a name="line.56"></a>
<FONT color="green">057</FONT>         * words, this method represents the (cumulative) distribution function<a name="line.57"></a>
<FONT color="green">058</FONT>         * (CDF) for this distribution.<a name="line.58"></a>
<FONT color="green">059</FONT>         *<a name="line.59"></a>
<FONT color="green">060</FONT>         * @param x the point at which the CDF is evaluated<a name="line.60"></a>
<FONT color="green">061</FONT>         * @return the probability that a random variable with this<a name="line.61"></a>
<FONT color="green">062</FONT>         * distribution takes a value less than or equal to {@code x}<a name="line.62"></a>
<FONT color="green">063</FONT>         */<a name="line.63"></a>
<FONT color="green">064</FONT>        double cumulativeProbability(double x);<a name="line.64"></a>
<FONT color="green">065</FONT>    <a name="line.65"></a>
<FONT color="green">066</FONT>        /**<a name="line.66"></a>
<FONT color="green">067</FONT>         * For a random variable {@code X} whose values are distributed according<a name="line.67"></a>
<FONT color="green">068</FONT>         * to this distribution, this method returns {@code P(x0 &lt; X &lt;= x1)}.<a name="line.68"></a>
<FONT color="green">069</FONT>         *<a name="line.69"></a>
<FONT color="green">070</FONT>         * @param x0 the exclusive lower bound<a name="line.70"></a>
<FONT color="green">071</FONT>         * @param x1 the inclusive upper bound<a name="line.71"></a>
<FONT color="green">072</FONT>         * @return the probability that a random variable with this distribution<a name="line.72"></a>
<FONT color="green">073</FONT>         * takes a value between {@code x0} and {@code x1},<a name="line.73"></a>
<FONT color="green">074</FONT>         * excluding the lower and including the upper endpoint<a name="line.74"></a>
<FONT color="green">075</FONT>         * @throws NumberIsTooLargeException if {@code x0 &gt; x1}<a name="line.75"></a>
<FONT color="green">076</FONT>         *<a name="line.76"></a>
<FONT color="green">077</FONT>         * @deprecated As of 3.1. In 4.0, this method will be renamed<a name="line.77"></a>
<FONT color="green">078</FONT>         * {@code probability(double x0, double x1)}.<a name="line.78"></a>
<FONT color="green">079</FONT>         */<a name="line.79"></a>
<FONT color="green">080</FONT>        @Deprecated<a name="line.80"></a>
<FONT color="green">081</FONT>        double cumulativeProbability(double x0, double x1) throws NumberIsTooLargeException;<a name="line.81"></a>
<FONT color="green">082</FONT>    <a name="line.82"></a>
<FONT color="green">083</FONT>        /**<a name="line.83"></a>
<FONT color="green">084</FONT>         * Computes the quantile function of this distribution. For a random<a name="line.84"></a>
<FONT color="green">085</FONT>         * variable {@code X} distributed according to this distribution, the<a name="line.85"></a>
<FONT color="green">086</FONT>         * returned value is<a name="line.86"></a>
<FONT color="green">087</FONT>         * &lt;ul&gt;<a name="line.87"></a>
<FONT color="green">088</FONT>         * &lt;li&gt;&lt;code&gt;inf{x in R | P(X&lt;=x) &gt;= p}&lt;/code&gt; for {@code 0 &lt; p &lt;= 1},&lt;/li&gt;<a name="line.88"></a>
<FONT color="green">089</FONT>         * &lt;li&gt;&lt;code&gt;inf{x in R | P(X&lt;=x) &gt; 0}&lt;/code&gt; for {@code p = 0}.&lt;/li&gt;<a name="line.89"></a>
<FONT color="green">090</FONT>         * &lt;/ul&gt;<a name="line.90"></a>
<FONT color="green">091</FONT>         *<a name="line.91"></a>
<FONT color="green">092</FONT>         * @param p the cumulative probability<a name="line.92"></a>
<FONT color="green">093</FONT>         * @return the smallest {@code p}-quantile of this distribution<a name="line.93"></a>
<FONT color="green">094</FONT>         * (largest 0-quantile for {@code p = 0})<a name="line.94"></a>
<FONT color="green">095</FONT>         * @throws OutOfRangeException if {@code p &lt; 0} or {@code p &gt; 1}<a name="line.95"></a>
<FONT color="green">096</FONT>         */<a name="line.96"></a>
<FONT color="green">097</FONT>        double inverseCumulativeProbability(double p) throws OutOfRangeException;<a name="line.97"></a>
<FONT color="green">098</FONT>    <a name="line.98"></a>
<FONT color="green">099</FONT>        /**<a name="line.99"></a>
<FONT color="green">100</FONT>         * Use this method to get the numerical value of the mean of this<a name="line.100"></a>
<FONT color="green">101</FONT>         * distribution.<a name="line.101"></a>
<FONT color="green">102</FONT>         *<a name="line.102"></a>
<FONT color="green">103</FONT>         * @return the mean or {@code Double.NaN} if it is not defined<a name="line.103"></a>
<FONT color="green">104</FONT>         */<a name="line.104"></a>
<FONT color="green">105</FONT>        double getNumericalMean();<a name="line.105"></a>
<FONT color="green">106</FONT>    <a name="line.106"></a>
<FONT color="green">107</FONT>        /**<a name="line.107"></a>
<FONT color="green">108</FONT>         * Use this method to get the numerical value of the variance of this<a name="line.108"></a>
<FONT color="green">109</FONT>         * distribution.<a name="line.109"></a>
<FONT color="green">110</FONT>         *<a name="line.110"></a>
<FONT color="green">111</FONT>         * @return the variance (possibly {@code Double.POSITIVE_INFINITY} as<a name="line.111"></a>
<FONT color="green">112</FONT>         * for certain cases in {@link TDistribution}) or {@code Double.NaN} if it<a name="line.112"></a>
<FONT color="green">113</FONT>         * is not defined<a name="line.113"></a>
<FONT color="green">114</FONT>         */<a name="line.114"></a>
<FONT color="green">115</FONT>        double getNumericalVariance();<a name="line.115"></a>
<FONT color="green">116</FONT>    <a name="line.116"></a>
<FONT color="green">117</FONT>        /**<a name="line.117"></a>
<FONT color="green">118</FONT>         * Access the lower bound of the support. This method must return the same<a name="line.118"></a>
<FONT color="green">119</FONT>         * value as {@code inverseCumulativeProbability(0)}. In other words, this<a name="line.119"></a>
<FONT color="green">120</FONT>         * method must return<a name="line.120"></a>
<FONT color="green">121</FONT>         * &lt;p&gt;&lt;code&gt;inf {x in R | P(X &lt;= x) &gt; 0}&lt;/code&gt;.&lt;/p&gt;<a name="line.121"></a>
<FONT color="green">122</FONT>         *<a name="line.122"></a>
<FONT color="green">123</FONT>         * @return lower bound of the support (might be<a name="line.123"></a>
<FONT color="green">124</FONT>         * {@code Double.NEGATIVE_INFINITY})<a name="line.124"></a>
<FONT color="green">125</FONT>         */<a name="line.125"></a>
<FONT color="green">126</FONT>        double getSupportLowerBound();<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>        /**<a name="line.128"></a>
<FONT color="green">129</FONT>         * Access the upper bound of the support. This method must return the same<a name="line.129"></a>
<FONT color="green">130</FONT>         * value as {@code inverseCumulativeProbability(1)}. In other words, this<a name="line.130"></a>
<FONT color="green">131</FONT>         * method must return<a name="line.131"></a>
<FONT color="green">132</FONT>         * &lt;p&gt;&lt;code&gt;inf {x in R | P(X &lt;= x) = 1}&lt;/code&gt;.&lt;/p&gt;<a name="line.132"></a>
<FONT color="green">133</FONT>         *<a name="line.133"></a>
<FONT color="green">134</FONT>         * @return upper bound of the support (might be<a name="line.134"></a>
<FONT color="green">135</FONT>         * {@code Double.POSITIVE_INFINITY})<a name="line.135"></a>
<FONT color="green">136</FONT>         */<a name="line.136"></a>
<FONT color="green">137</FONT>        double getSupportUpperBound();<a name="line.137"></a>
<FONT color="green">138</FONT>    <a name="line.138"></a>
<FONT color="green">139</FONT>        /**<a name="line.139"></a>
<FONT color="green">140</FONT>         * Whether or not the lower bound of support is in the domain of the density<a name="line.140"></a>
<FONT color="green">141</FONT>         * function.  Returns true iff {@code getSupporLowerBound()} is finite and<a name="line.141"></a>
<FONT color="green">142</FONT>         * {@code density(getSupportLowerBound())} returns a non-NaN, non-infinite<a name="line.142"></a>
<FONT color="green">143</FONT>         * value.<a name="line.143"></a>
<FONT color="green">144</FONT>         *<a name="line.144"></a>
<FONT color="green">145</FONT>         * @return true if the lower bound of support is finite and the density<a name="line.145"></a>
<FONT color="green">146</FONT>         * function returns a non-NaN, non-infinite value there<a name="line.146"></a>
<FONT color="green">147</FONT>         * @deprecated to be removed in 4.0<a name="line.147"></a>
<FONT color="green">148</FONT>         */<a name="line.148"></a>
<FONT color="green">149</FONT>        boolean isSupportLowerBoundInclusive();<a name="line.149"></a>
<FONT color="green">150</FONT>    <a name="line.150"></a>
<FONT color="green">151</FONT>        /**<a name="line.151"></a>
<FONT color="green">152</FONT>         * Whether or not the upper bound of support is in the domain of the density<a name="line.152"></a>
<FONT color="green">153</FONT>         * function.  Returns true iff {@code getSupportUpperBound()} is finite and<a name="line.153"></a>
<FONT color="green">154</FONT>         * {@code density(getSupportUpperBound())} returns a non-NaN, non-infinite<a name="line.154"></a>
<FONT color="green">155</FONT>         * value.<a name="line.155"></a>
<FONT color="green">156</FONT>         *<a name="line.156"></a>
<FONT color="green">157</FONT>         * @return true if the upper bound of support is finite and the density<a name="line.157"></a>
<FONT color="green">158</FONT>         * function returns a non-NaN, non-infinite value there<a name="line.158"></a>
<FONT color="green">159</FONT>         * @deprecated to be removed in 4.0<a name="line.159"></a>
<FONT color="green">160</FONT>         */<a name="line.160"></a>
<FONT color="green">161</FONT>        boolean isSupportUpperBoundInclusive();<a name="line.161"></a>
<FONT color="green">162</FONT>    <a name="line.162"></a>
<FONT color="green">163</FONT>        /**<a name="line.163"></a>
<FONT color="green">164</FONT>         * Use this method to get information about whether the support is connected,<a name="line.164"></a>
<FONT color="green">165</FONT>         * i.e. whether all values between the lower and upper bound of the support<a name="line.165"></a>
<FONT color="green">166</FONT>         * are included in the support.<a name="line.166"></a>
<FONT color="green">167</FONT>         *<a name="line.167"></a>
<FONT color="green">168</FONT>         * @return whether the support is connected or not<a name="line.168"></a>
<FONT color="green">169</FONT>         */<a name="line.169"></a>
<FONT color="green">170</FONT>        boolean isSupportConnected();<a name="line.170"></a>
<FONT color="green">171</FONT>    <a name="line.171"></a>
<FONT color="green">172</FONT>        /**<a name="line.172"></a>
<FONT color="green">173</FONT>         * Reseed the random generator used to generate samples.<a name="line.173"></a>
<FONT color="green">174</FONT>         *<a name="line.174"></a>
<FONT color="green">175</FONT>         * @param seed the new seed<a name="line.175"></a>
<FONT color="green">176</FONT>         */<a name="line.176"></a>
<FONT color="green">177</FONT>        void reseedRandomGenerator(long seed);<a name="line.177"></a>
<FONT color="green">178</FONT>    <a name="line.178"></a>
<FONT color="green">179</FONT>        /**<a name="line.179"></a>
<FONT color="green">180</FONT>         * Generate a random value sampled from this distribution.<a name="line.180"></a>
<FONT color="green">181</FONT>         *<a name="line.181"></a>
<FONT color="green">182</FONT>         * @return a random value.<a name="line.182"></a>
<FONT color="green">183</FONT>         */<a name="line.183"></a>
<FONT color="green">184</FONT>        double sample();<a name="line.184"></a>
<FONT color="green">185</FONT>    <a name="line.185"></a>
<FONT color="green">186</FONT>        /**<a name="line.186"></a>
<FONT color="green">187</FONT>         * Generate a random sample from the distribution.<a name="line.187"></a>
<FONT color="green">188</FONT>         *<a name="line.188"></a>
<FONT color="green">189</FONT>         * @param sampleSize the number of random values to generate<a name="line.189"></a>
<FONT color="green">190</FONT>         * @return an array representing the random sample<a name="line.190"></a>
<FONT color="green">191</FONT>         * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException<a name="line.191"></a>
<FONT color="green">192</FONT>         * if {@code sampleSize} is not positive<a name="line.192"></a>
<FONT color="green">193</FONT>         */<a name="line.193"></a>
<FONT color="green">194</FONT>        double[] sample(int sampleSize);<a name="line.194"></a>
<FONT color="green">195</FONT>    }<a name="line.195"></a>




























































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